1. Soil Stress and Pore Water Pressure
UNIT II

2. Stress Distribution in Soils
By: Kamal Tawfiq, Ph.D., P.E
Added
Stress
Stress Distribution in Soils
Geostatic
Stress
Added Stresses (Point, line, strip, triangular, circular, rectangular)
Geostatic Stresses
Total Stress
Effective Stress
Pore Water Pressure
Westergaard’s Method
(For Pavement)
Bossinisque Equations
Point Load
Line Load
Strip Load
Triangular Load
Circular Load
Rectangular Load
Approximate Method
1:2 Method sy sx
txy
Total Stress= Effective Stress+ Pore Water Pressure
stotal = seff + u
Stress Bulbs
Influence Charts
Newmark Charts A

3. SOIL WATER AND WATER FLOW
Soil water – static pressure in water - Effective stress concepts in soils – capillary stress – Permeability measurement in the laboratory and field pumping in pumping out tests – factors influencing permeability of soils – Seepage – introduction to flow nets – Simple problems. (sheet pile and weir).

4. Soil Stress and Pore Water Pressure
The total vertical stress (σv) acting at a point below the ground surface is due to the weight of everything lying above i.e. soil, water, and surface loading
Total vertical stresses are calculated from the unit weight of the soil
Any change in total vertical stress (σv) may also result in a change in the horizontal total stress (σ h) at the same point
The relationships between vertical and horizontal stress are complex (Δσv ≠ Δσh)

5. TOTAL VERTICAL STRESS in homogeneous soil
Ground Level
SOIL
ELEMENT σv
Depth, z

6. TOTAL VERTICAL STRESS below a river or lake
Water Level zw
Ground Level z

7. TOTAL VERTICAL STRESS in multi-layered soil
Ground Level z1
Soil1 z2
Soil2 z3
Soil3

8. TOTAL VERTICAL STRESS with a surface surcharge load
Very ‘wide’ surcharge, q (kN/m2)
Ground Level z

9. PORE WATER PRESSURE
The water in the pores of a soil is called pore water.
The pressure within this porewater is called pore water pressure (u)
The magnitude of pore water pressure depends on:
the depth below the water table
the conditions of seepage flow

10. PORE WATER PRESSURE under hydrostatic conditions (no water flow)
Ground Level
Water Table z

11. EFFECTIVE STRESS CONCEPT (Terzaghi, 1923)
where
= Total Vertical Stress
= Effective Stress
= Pore Water Pressure

12. VERTICAL EFFECTIVE STRESSES
Water Table
Ground Level z

13. EXAMPLE 1
Plot the variation of total and effective vertical stresses, and pore water pressure with depth for the soil profile shown below
Ground Level
Water Table
kN/m3
GRAVELY SAND 4m
kN/m3 2m 4m
SAND
kN/m3 5m
SAND GRAVEL
kN/m3

14. EXAMPLE 2 The soil layers on a site consists of:
0 – 4 m Gravel-sand (ρsat= 2038 kg/m3; ρB 1957 kg/m3)
4 – 9 m Clay (ρsat= 1835 kg/m3)
Draw an effective stress and total stress profile between 0 – 9m, when the water table is 1m above the top of the clay

15. EXAMPLE 3
On a certain site a surface layer of silty sand is 4m thick and overlies a layer of peaty clay 7m thick, which in turn is underlain by impermeable rock. Draw effective and total stress profiles for the following condition:
Water table at the surface
Water table at a depth of 5m, with the silty sand above the water table saturated with capillary water
Unit weight:
Silty Sand = 18.5 kN/m3
Clay = 17.7 kN/m3

16. EXAMPLE 4
A confined aquifer comprises a 5m thick of sand overlain by a 4m thick layer of clay and underlain by impermeable rock. The unit weight of the sand and clay respectively are 19.6 kN/m3 and 18.4 kN/m3. Determine effective overburden stress at the top and bottom of the sand layer, when the levels of the water in a standpipe driven through the clay into the sand layer are:
at ground surface
1.5m below the ground surface
3.0m below the ground surface
1.5m above the ground surface
3.0m above the ground surface
and hence comment on the effect of changing water table

17. EXAMPLE 5
A sediment settling lagoon has a depth of water of 4m above the clay base. The clay layer is 3m thick and this overlies 4m of a medium sand, which in turn overlies impermeable rock. Calculate the effective stresses at the top of the clay and at the top and bottom of the second layer under the following condition:
Initially, before any sediment is deposited
After a 3m layer of sediment of silty fine sand has been deposited
After draining the lagoon down to base level, with same thickness (3m) of sediment still in place
Unit weight:
Sand = 20 kN/m3; Clay = 18 kN/m3; Sediment = 16 kN/m3

18. EXAMPLE 6
Plot the variation of total and effective vertical stresses, and pore water pressure with depth for the soil profile shown below for the following condition:
initially before construction
immediately after construction
few days after construction
many years after construction.
Surface surcharge, q (100 kN/m2)
Ground Level
Water Table
kN/m3 4m
SAND 2m
CLAY
kN/m3

19. SHORT TERM & LONG TERM STRESSES
Initially before construction
Stress distribution profile at its original stage
Immediately after construction
The immediately effect after the construction is an increasing in the pore water pressure – loading is too rapid and not allow any significant out flow of pore water and the soils are in an UNDRAINED stage
Few days after construction
Few days after the construction, the out flow of pore water takes place at the Sand layer due to its high permeability and the sand is in DRAINED stage. i.e. excess PWP is dissipated at the Sand layer whereas Clay Layer is in contrast
Many years after construction
After many years, excess PWP will dissipated in clay layer despite its low permeability and the soils are in drained stage

20. Hydraulic Conductivity
The ease with which water moves through soils
Strongly responsible for water distribution
within the soil volume.
Determines the rate of water movement in soil.
Texture
Density
Structure
Water content

21. Texture
Density
Structure
Water content
Texture – small particles = small pores = poor conductivity
Density – high density suggests low porosity and small pores
Structure – inter-aggregate macro pores improve conductivity
Water content – water leaves large pores first.
At lower water contents, smaller pores conduct water, reducing conductivity.
Maximum conductivity is under saturated conditions.

22. Hydraulic Conductivity
Coarse
Un compacted
Fine
compacted

23. Ponded Water
High conductivity
Sand
Clay
low conductivity

24. Measuring Saturated Hydraulic ConductivityW A T E R
Volume
time
h * A L h S o I L L A
Flow Volume

25. = K Volume h * A time L Volume h * A time L K = V * L h * A * t L
soil h L
Vwater
Volume
time
h * A L
Volume
time
= K
h * A L
Solve for K
K = V * L
h * A * t

26. Constant Head Apparatus

27. L is length through the soil
y is the height of ponded water
x is the height of water required to lower the gradient so that y can be maintained.
Note: if the gradient is 1 then Ks = q as per Darcy’s Law.

28. Falling Head Apparatus

29. a is the cross-sectional area of the burette
A is the cross-sectional area of the soil column
t2 – t1 is the time required for the head to drop from H1 to H2.